Simplify the Expression: a+b-(2c+b) Step by Step

Algebraic Simplification with Parentheses and Signs

a+b(2c+b)=? a+b-(2c+b)=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Note that when multiplying negative by positive, the result is always negative:
00:19 Let's group the factors
00:28 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

a+b(2c+b)=? a+b-(2c+b)=\text{?}

2

Step-by-step solution

First, we open the parentheses and change the sign accordingly.

Since there are only positive numbers inside the parentheses, multiplying by negative will give us negative numbers:

a+b2cb= a+b-2c-b=

Now we group the b factors:

bb=0 b-b=0

Now we obtain:

a2c a-2c

3

Final Answer

a2c a-2c

Key Points to Remember

Essential concepts to master this topic
  • Distribution Rule: Distribute the negative sign to all terms inside parentheses
  • Technique: Transform -(2c+b) into -2c-b before combining like terms
  • Check: Substitute values: if a=3, b=2, c=1, then 3+2-(2+2)=1 and 3-2=1 ✓

Common Mistakes

Avoid these frequent errors
  • Not distributing the negative sign to all terms
    Don't change -(2c+b) to just -2c+b! The negative must distribute to BOTH terms inside parentheses, giving -2c-b. Forgetting this gives wrong answers like a+2b-2c instead of a-2c. Always distribute the negative sign to every single term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

\( 100-(30-21)= \)

FAQ

Everything you need to know about this question

Why does the b disappear in the final answer?

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Great observation! When we distribute the negative sign, we get a+b2cb a+b-2c-b . The terms +b and -b are opposites that cancel each other out: b - b = 0.

What if there was a number in front of the parentheses?

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You'd multiply that number by every term inside the parentheses! For example, 3(2c+b)=6c+3b 3(2c+b) = 6c+3b . The distributive property always applies to all terms.

How do I know which terms are like terms?

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Like terms have the same variable parts. In this problem, we have two b terms: +b and -b. The terms a and c don't have matching partners, so they stay as is.

Can I work from right to left instead?

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You should follow the order of operations! Handle what's in parentheses first, then distribute, then combine like terms from left to right. This prevents mistakes.

What if I get confused about the signs?

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Write out each step carefully! Change (2c+b) -(2c+b) to +(2c)+(b) +(-2c)+(-b) which equals 2cb -2c-b . Taking your time prevents sign errors.

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